Radical Data Compression Algorithm Using Factorization

Zirra Peter Buba & Gregory Maksha Wajiga
International Journal of Computer Science and Security (IJCSS), Volume (5) : Issue (2) : 2011 221
Radical Data Compression Algorithm Using Factorization
Zirra Peter Buba zirrapeter@yahoo.com
Department of Mathematical Sciences
Adamawa State University
Mubi, 650221, Nigeria.
Gregory Maksha Wajiga gwajiga@gmail.com
Department of Mathematics and Computer Science
Federal University of Technology
Yola, 640284, Nigeria.
Abstract
This work deals with encoding algorithm that conveys a message that generates a “compressed”
form with fewer characters only understood through decoding the encoded data which
reconstructs the original message. The proposed factorization techniques in conjunction with
lossless method were adopted in compression and decompression of data for exploiting the size
of memory, thereby decreasing the cost of the communications. The proposed algorithms shade
the data from the eyes of the cryptanalysts during the data storage or transmission.
Keywords: Data Compression, Cryptography, Lossless, Algorithm
1. INTRODUCTION
In this paper the generic term message is used for the object to be compressed. Compression
consists of two components, an encoding algorithm that takes a message and generates a
“compressed” representation (with fewer characters), and a decoding algorithm that reconstructs
the original message from the compressed representation.
There are "lossless" and "lossy" forms of data compression [1]. Lossless (reversible) data
compression is used when the data has to be uncompressed exactly as it was before
compression. Text files are stored using lossless techniques, since losing a single character can
in the worst case make the text dangerously misleading. Archival storage of master sources for
images, video, and audio data generally needs to be lossless as well. However, there are strict
limits to the amount of compression that can be obtained with lossless compression.
Lossy (irreversible) compression, in contrast, works on the assumption that the data doesn't have
to be stored perfectly. Much information can be simply thrown away from images, video, and
audio data, and when uncompressed, such data will still be of acceptable quality. Compression
ratios can be an order of magnitude greater than those available from lossless methods [2].
The proposed factorization techniques of data compression uses lossless method of compressing
and decompressing of data to exploit the size of memory, thereby decreasing the cost of the
communications and shading the data from the eyes of the cryptanalysts during the data storage
or transmission.
2. DATA COMPRESSION
Data compression is defined as the reduction of the volume of a data file without loss of
information [3]. As pointed out by [4] and [5], data compression aims to condense the data in
order to reduce the size of a data file.
Data compression has important application in the areas of data transmission and data storage
[6]. Many data processing applications require storage of large volumes of data, and the number
of such applications is constantly increasing as the use of computers extends to new disciplines.

At the same time, the proliferation of computer communication networks is resulting in massive
transfer of data over communication links. Compressing data to be stored or transmitted reduces
storage and communication costs. When the amount of data to be transmitted is reduced, the
effect is that of increasing the capacity of the communication channel [7]. Similarly, compressing
a file to half of its original size is equivalent to doubling the capacity of the storage medium. It may
then become feasible to store the data at a higher, thus faster, level of the storage hierarchy and
reduce the load on the input/output channels of the computer system.
3. THEORETICAL FRAME WORK
The main feature of the radical data compression algorithm takes as an input a plaintext,
compress the string of the characters and produce an output in ciphertext. To decompress, the
ciphertext requires a decompression key [8]. The decompression key is transmitted to the
receiver through different media such as email or Short Message Service (SMS) to strengthen its
security. The whole process is depicted in Figure 1.
4. THE PROPOSED RADICAL COMPRESSION ALGORITHMS
4.1 Compression Algorithm
The compression of the data is achieved through the following:
i. Each character or symbol in the message such as number, white space and punctuation
are assigned a numerical value.
ii. The encoding scheme in Table 1 is employed.
4.1.1 Compression Key
a. Serialization of string.
b. Write down character of the input string without repetition.
c. The encoding scheme in Table 1.
FIGURE 1: Compression and Decompression Process

Symbol Count Locations Product Sum Maximum Location
TABLE 1: Encoding Scheme
Illustrative example 1: If we are going to compress the random message “WHO IS PROMISSING
WHO”, we would have an encoded message that is given in Table 3 using Table 2.
S/No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Symbol W H O I S P R O M I S I N G W H O
TABLE 2: Serialization of plaintext
Symbol
White
space
W H O I S P R M N G
Location 4,7,17
1,18 2,19 3,10,20 5,12,14 6,13 8 9 11 15 16
Character
Count
3
2 2 3 3 2 1 1 1 1 1
Sum 28
19 21 33 31 19 8 9 11 15 16
Product 476
18 38 600 840 78 8 9 11 15 16
Maximum
Location
17
18 19 20 14 13 8 9 11 15 16
TABLE 3: Encoded Symbols
Hence the compressed data is WHOISPRMNG and a white space.
We can easily find where characters ‘white space’, ‘G’,’H’, ‘I’, ‘M’, ‘N’, and so on occurred in the
message by exploring the compression algorithm in section 4.2 visa vice Table 3.
4.2 Decompression Algorithm
The algorithm, which describes each step in compression process, is listed in the
Algorithm_Decompression (input: symbol) below
Algorithm_Decompression (input: symbol)
Step 1: Read the product , sum and the maximum occurrence of the
character as produced in Table 3.

Step 2: Begin
Step 3: If , then output
Step 4: Else
Step 5: Compute factor(s) of such that the factor(s) satisfy the
value
Step 6: Endif
Step 7: If (3) or (5) is true, then output the character at location(s) ( )
Step 8: Else goto step 5
Step 9: Repeat steps (1) to (8) for until
Step 10: EndBegin
EndAlgorith_Decompression
4.2.1 Decompression key
factors of such that the factor(s) satisfy the values of and in Table 3 or if
write .
This key is transmitted through a different channel (email) to the recipient in order to be able to
decompress the characters.
Illustrative example 2: To decode the character symbol ‘white space’:
From the Algorithm_Decompression (input: symbol), the computed value of , ,
, and , as depicted in Table 3.
a) We compute the factors of , which are 1, 2, 4, 7, 14 and 17
b) From (a) we take factors of that satisfied the value of . These are 4, 7
and 17.
Since the value of are satisfied, a blank space is created at locations 4, 7 and 17.
Taking the second character symbol G: the value , , , and
c) We compute the factors of , which are 1 and 16.
d) From (c) we take factors of that satisfied the value of and that is
Since the value of are satisfied, a character G is written at locations 16 only.
Similarly, to decode the character symbol “H”, we take the value of , , , and
, from the Algorithm_Decompression (input: symbol).
e) We compute the factors of , which are 1, 2 and 19
f) From (e) we take factors of that satisfied the value of . These are 2
and 19
Since the value of are satisfied, the character “H” is printed at locations 2.
This is continued until all the characters of the plaintext have been recovered to its original
plaintext “WHO IS PROMISING WHO” as depicted in Table 2.
5. RESULTS AND DISCUSSION
From Table 3, and the results of illustrative example 2, showed how efficient and practicable [9]
the proposed data compression scheme in Table 1 and decompression algorithms in section 4.2
in handling any kinds of plaintext in an unsecure channel and how it increases storage capacity
for faster data processing [3].

The meaningless results in Table 3 is in line with the proposed data compression and
decompression algorithms which helped to conceal the content of sensitive information from the
terrorist [9,10]. These meant that the proposed algorithms has proved to prevent the hacker from
gaining insight of what the content of information was all about while in either transit or store.
The result of the study has also successfully reduced the large volume of the plaintext that
contained the same information as the original string in Table 2 but whose length was small as
possible [3,4,7]. These proved that it may then become feasible to store the data at a higher,
faster, level of the storage hierarchy [5] and reduce the load on the input/output channels of the
computer systems which is the main goal of data compression techniques [11,12].
The results of the study also shown that one key is used for encoding the data and another
different key were used for decoding of the data. The results revealed that the receiver obtained
these key from the sender secretly through either SMS or Fax machine. The strength of
cryptography systems in the computer era rests on the secrecy of the key, not on the algorithm
[8]. It is clear that our information is not easily visible to an unauthorized person without a
decoding key. The concealment of the key rather than the encryption technique is one of the most
important features of a strong cryptography system [10].
6. CONCLUSION
The new data compression transforms a string of characters into a new string (encoded) using
compression key and reverses the encoded string using decompression key. The encoded string
contains the same information as the original string but whose length is small as possible. These
shade the information contents from the eyes of the intruders, but thereby increasing the capacity
of the communication channel. Therefore, the algorithms will be found useful by organizations
that deal with sensitive documents.
7. REFERENCES
[1] W.S. Steven.The Scientist and Engineer’s Guide To Digital Signal Processing. Califonia:
Technical Publishing, 2007.
[2] E. B. Guy. “Introduction to Data Compression”. Internet: www. eecs.harvard.
edu/~michaelm /CS222/ compression.pdf, 2010 [Jan. 24, 2011].
[3] A.G. Fraser. “Data Compression and Automatic Programming”. Internet:
www.comjnl.oxfordjournals.org, 2010 [Oct. 16, 2010].
[4] N. Ziviani, E. Moura, G. Navarro, and R. Baeza-Yates. “Compression: A key for
next generation text retrieval systems”. IEEE Computer Society, 2000, 33(11), pp. 37- 44.
2000
[5] A. Kattan. “Universal lossless compression technique with built in encryption”. M. Sc.
Thesis, University of Essex, UK., 2006.
[6] S. Khalid. Introduction to Data Compression (2nd ed.) New York : Morgan Kaufmann
Publishers Inc., 2000, pp 151-218.
[7] E.J.D. Garba and S.E Adewumi. “A Cryptosystems Algorithm Using Systems of Nonlinear
Equations”. Iranian Journal of Information Science And Technology, 2003, 1(1), pp. 43-
55.
[8] M. Milenkovic. Operating System: Concepts and Design, New York: McGrew-Hill, Inc.,
1992.

[9] V. Singla, R. Singla, and S. Gupta. “Data Compression Modelling: Huffman and
Arithmetic” International Journal of The Computer, the Internet and Management, 2008,
16(3), pp 64- 68
[10] Cryptography FAQ (03/10: Basic Cryptology), "3.5. What are some properties satisfied by
every strong cryptosystem?" [cited 23 August 2006]; Available:
http://www.faqs.org/faqs/cryptographyfaq/part03/index.html.
[11] A. Hauter, M.V.C., R. Ramanathan. Compression and Encryption. CSI 801 Project Fall
1995. December 7, 1995 [cited 10 March2006];
Available: http://www.science.gmu.edu/~mchacko/csi801/proj-ckv.html.
[12] How does cryptography work. 12 March 2006 [cited 12 March 2006 ];
Available: http://www.pgpi.org/doc/pgpintro.

Radical Data Compression Algorithm Using Factorization

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